Abstract
In this article, we consider the following systems of Fredholm integral equations: Using an argument originating from Brezis and Browder [Bull. Am. Math. Soc. 81, 73-78 (1975)] and a fixed point theorem, we establish the existence of solutions of the first system in (C[0, T]) n , whereas for the second system, the existence criteria are developed separately in (C l [0,∞)) n as well as in (BC[0,∞)) n . For both systems, we further seek the existence of constant-sign solutions, which include positive solutions (the usual consideration) as a special case. Several examples are also included to illustrate the results obtained. 2010 Mathematics Subject Classification: 45B05; 45G15; 45M20.
Highlights
In this article, we shall consider the system of Fredholm integral equations: ui(t) = hi(t) + gi(t, s)fi(s, u1(s), u2(s), . . . , un(s))ds, t ∈ [0, T], 1 ≤ i ≤ n (1:1)where 0 < T
1 Introduction In this article, we shall consider the system of Fredholm integral equations: T
Note that when θi = 1 for all 1 ≤ i ≤ n, a constant-sign solution reduces to a positive solution, which is the usual consideration in the literature
Summary
We shall consider the system of Fredholm integral equations: ui(t) = hi(t) + gi(t, s)fi(s, u1(s), u2(s), . We shall tackle the existence of constant-sign solutions of (1.1) and (1.2). There is a vast amount of research on the existence of positive solutions of the nonlinear Fredholm integral equations: y(t) = h(t) + g(t, s)f (y(s))ds, t ∈ [0, T]. A generalization of (1.3) and (1.4) to systems similar to (1.1) and (1.2) have been made, and the existence of single and multiple constant-sign solutions has been established for these systems in [6,7,8,9,10].
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